### Add questions

parent 73b8a8b8
_psets/7.md 0 → 100644
 --- title: Problem Set 7 --- ## (9.1) {:.question} Optics (as well as most of physics) can be derived from a global law as well as a local one, in this case Fermat’s Principle: a light ray chooses the path between two points that minimizes the time to travel between them. Apply this to two points on either side of a dielectric interface to derive Snell’s Law. ## (9.2) ### (a) {:.question} Use Fresnel’s equations and the Poynting vectors to find the reflectivity and transmissivity of a dielectric interface, defined by the ratios of incoming and outgoing energy. ### (b) {:.question} For a glass–air interface (n = 1.5) what is the reflectivity at normal incidence? ### (c) {:.question} What is the Brewster angle? ### (d) {:.question} What is the critical angle? ## (9.3) {:.question} Consider a wave at normal incidence to a dielectric layer with index \$\$n_2\$\$ and thickness \$\$d\$\$ between layers with indices \$\$n_1\$\$ and \$\$n_3\$\$. ### (a) {:.question} What is the reflectivity? Think about matching the boundary conditions, or about the multiple reflections. ### (b) {:.question} Can you find values for \$\$n_2\$\$ and \$\$d\$\$ such that the reflection vanishes? ## (9.4) {:.question} Consider a ray starting with a height \$\$r_0\$\$ and some slope, a distance \$\$d_1\$\$ away from a thin lens with focal length \$\$f\$\$. Use ray matrices to find the image plane where all rays starting at this point rejoin, and discuss the magnification of the height \$\$r_0\$\$. ## (9.5) {:.question} Common CD players use an AlGaAs laser with a 790 nm wavelength. ### (a) {:.question} The pits that are read on a CD have a diameter of roughly \$\$1 \si{\mu m}\$\$ and the optics are diffraction-limited; what is the beam divergence angle? ### (b) {:.question} Assuming the same geometry, what wavelength laser would be needed to read \$\$0.1 \si{\mu m}\$\$ pits? ### (c) {:.question} How large must a telescope mirror be if it is to be able to read a car’s license plate in visible light (\$\$\lambda \approx 600 \si{nm}\$\$) from a Low Earth Orbit (LEO) of 200 km?
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment